Method for characterizing the accuracy of a simulated electrical circuit model

ABSTRACT

Methods are disclosed for quantitatively characterizing the accuracy of a simulated electrical circuit model. In particular, available circuit simulation programs make use of “black box” models of transmission lines used to carry high-speed electrical signals. Electrical transmission lines are characterized by resistance, inductance, capacitance, and dielectric conductance, all values of which may vary with frequency. The “black box” model must accurately model the transmission line over a wide range of frequencies in a time-domain simulation. Algorithms used in the “black box” model may not accurately model the transmission line over the frequency range. Such inaccuracies must be quantified, and if excessive, must be corrected.

FIELD OF THE INVENTION

[0001] The present invention relates to circuit simulation models. Inparticular, the present invention relates to transmission line modelsused in the process of simulating high-speed signal transmission.

DESCRIPTION OF RELATED ART

[0002] Historically, electronic systems, and in particular, computersystems, comprise a number of semiconductor chips, upon which circuitryis placed. That circuitry performs the desired logic and other functionsrequired by the electronic system. For example, the chips in a computersystem have logical circuitry which performs AND, OR, and latchfunctions, for example. These and other circuitry are coupled togetherto create, for example, Arithmetic Logic Units (ALUs), Floating PointUnits (FPUs), memories in various levels of memory hierarchies, andcontrollers. Modern electronic systems utilize a vast range ofelectronic circuit functions, and the above examples represent but asmall sample of such circuitry.

[0003] The chips are typically mounted on modules, which are typicallyfurther mounted on Printed Wiring Boards (PWBs). The PWBs are coupledtogether with cables, or by plugging the PWBs into yet another level ofPWB.

[0004] The chips are coupled together by signal conductors that carrysignals from one chip to another. Signal conductors may couple chipsmounted on the same module, in the case of a Multi-Chip Module (MCM)packaging arrangement. In addition, signal conductors may also couplechips on different modules, and different PWBs depending oninterconnection requirements of the system.

[0005] Signal conductors used in modern electronic systems are designedas transmission lines. Transmission lines have a conductor for carryingthe signal, and a nearby conducting path for carrying return current.Transmission lines intended to carry high frequency signals areelectrically modeled with an “RLCG” (series Resistance per unit length(R); series inductance per unit length (L); parallel capacitance perunit length (C); and parallel conductance per unit length (G). Suitableunits for these modeling elements are chosen. For example, resistance inohms/cm; inductance in henries/cm; capacitance in farads/cm; andconductance in siemens/cm would be a compatible set of units, whenvoltage is measured in volts, and electrical current is measured inamps. Many textbooks describe transmission lines and their mathematicalequations. For example, “High Speed Digital Design”, by Howard Johnsonand Martin Graham, ® 1993 by Prentice Hall PTR, ISBN 0-1-3395724-1describes transmission lines in some detail (hereinafter “Johnson”)

[0006] Each of the RLCG elements may be frequency dependent, andaccurate characterization and modeling of each element is a requirementwhen simulating the very high-speed signals used in modern electronicsystems. Such signals comprise frequency components of many gigahertz.For example, the resistance of the signal conductor is a strong functionof frequency. Typical transmission line modeling should includeresistance frequency effects for frequency components over 100 megahertz(MHz), and certainly, for frequency components over 1 gigahertz (GHz).L, C, and G are also dependent upon frequency.

[0007] Signals transmitted on a transmission line typically stay at alow level for a period of time, have very fast rise times, stay at ahigh level for a second period of time, and then have a very fast falltime to the low level. These signals have an extremely wide range offrequency components. Failure to accurately model all significantfrequency components of the signal in a computer model will result in aninaccurate simulation of the signal as it moves on the transmissionline. Optimizing the design of high-performance electronic systemsrelies on the accuracy of electrical circuit models and circuitsimulators. The quantitative results from circuit simulators are reliedupon to determine performance and reliability limits during all criticalphases of the system design. Based on these simulations, high-levelbusiness commitments are made long before hardware is available.Reliance on a model that fails to accurately model the RLCGcharacteristics of a transmission line, including frequency effects,can, and has, resulted in constructing electronic hardware that does notoperate correctly. Alternatively, knowingly using unreliable modelsleads designers to be extremely conservative in their designs, and nottaking full advantage of the technology they are using and paying for.

[0008] Computerized software circuit simulators, such as InternationalBusiness Machines Corporation's PowerSPICE, and Synopsys Corporation's,Star-Hspice™, allow “black box” models for transmission lines.PowerSPICE calls its “black box” an Rline; Star-Hspice™ calls its “blackbox” a W-element model. Hereinafter, such a “black box” model of atransmission line will simply be referred to as an Rline model, and suchreference is intended to apply to any “black box” model of atransmission line that receives, as inputs, frequency dependent RLCGspecifications. A user, or technology provider, provides the Rline modelwith tables, or expressions, for R, L, C, and G, versus frequency foreach type of transmission line of interest in a particular simulation.

[0009] The Rline model uses user-supplied frequency tables orexpressions that specify how the RLCG change as a function of frequency.This RLCG data is obtained, typically, from a field solver that examinesthe geometrical construction of the transmission line, appliesengineering knowledge of how the geometries involved determine the RLCGelements, and output the RLCG values for use as input to the Rlinemodel. The Rline model is then responsible for taking time-domainwaveforms of signals on ends of the transmission line, using thefrequency characteristics from the RLCG values, and yielding atime-domain response on ends of the transmission line. The time-domaincircuit simulator may be providing the Rline model with discrete inputvoltage and current values at particular simulation time intervals; thetime intervals may vary in length. As stated above, signals, especiallythe transitions of the signals, comprise an extremely wide range offrequencies. The task of creating accurate time-domain responses fromtime-domain signals using frequency dependent RLCG tables is extremelycomplex and difficult, involving curve fitting, convolution, and othernumerical techniques, and modeling errors can easily occur.

[0010] Validation of an Rline model has been a difficult task, involvingqualitative, empirical experience-based observations and insight basedon complex attempts to correlate circuit simulation waveforms withhardware laboratory measurements. Although useful and insightful, thesemethods involved many unknown variables that limited the ability to makea definitive quantitative assessment of just the Rline model interactingwith the circuit simulator. No prior art that uses circuit simulationtechniques to validate and quantify the model input to simulator outputaccuracy in a closed-loop fashion is known to exist. Even if one is ableto obtain a good time-domain graph of a high-speed input to a physicaltransmission line, together with the resulting output of thetransmission line for comparison with the modeled input and output, itis difficult to determine reasons for error. Validation of an Rlinemodel for all frequencies of interest has been a chronic problem.

[0011] Therefore, there is a need for a method that uses circuitsimulation techniques to validate and quantify the model input tosimulator output accuracy for an Rline model.

SUMMARY OF THE INVENTION

[0012] The present invention discloses a method of validating an Rlinemodel used by a time-domain circuit simulator by comparing a set offrequency dependent resistance, inductance, capacitive, and conductancevalues (RLCG values) provided as input to the Rline model with a set ofcomputed RLCG values output derived from the Rline model. The methodprovides a quantitative assessment of inaccuracies of the Rline model atfrequencies of interest.

[0013] An embodiment of the method comprises simulation of two instancesof the Rline model by a circuit simulator. The embodiment terminates anoutput of a first instance of the Rline model with an ideal terminator;providing a sinusoidal input signal of a first frequency to an inputport on the first instance of the Rline model; and observing a responseto the signal at the output port of the first instance of the Rlinemodel. A second instance of the Rline model has a first port and asecond port shorted together; the first and second ports further coupledto a sinusoidal input signal of the first frequency; current through thesinusoidal input signal is observed. Although different frequenciescould be used as input to the two instances of the Rline, computation ofthe output RLCG values is greatly simplified by applying the samefrequency to both instances of the Rline model. The method furthercomputes output RLCG values that would produce the response, andcompares the computed (output) RLCG values with the input RLCG valuesthat were used as input to the Rline model for the first frequency, todetermine, quantitatively, the accuracy of the Rline model, at thefrequency selected.

[0014] An embodiment of the method further comprises iteration of theabove embodiment for a number of frequencies, computing the output RLCGvalues that would produce the response at each frequency used, andcomparing the computed output RLCG values with the corresponding inputRLCG values of the input at each frequency, to determine thequantitative error of the Rline at each frequency.

[0015] In an embodiment, input RLCG values are plotted on a graph versusfrequency. Computed output RLCG values are plotted on a graph;advantageously, the same graph, versus frequency. Such an embodimentallows ready comparison of computed output RLCG characteristics withinput RLCG specifications, even if the frequencies used in simulationare not the same frequencies as those of the input RLCG input.Furthermore, simulations can be done at more or fewer frequencies thanare specified in the input RLCG input. Of particular value is a graph ofoutput RLCG values at a large number of frequencies, reducing thechances that the Rline model has an error that only occurs in a verysmall range of frequencies. Use of mathematical expressions,interpolations or equations, rather than graphical depiction, forcomparison of the input RLCG and the computed RLCG values are within thespirit and scope of this invention.

BRIEF DESCRIPTION OF THE DRAWINGS

[0016]FIG. 1A shows a circuit equivalent of a segment of a transmissionline.

[0017]FIG. 1B shows the circuit equivalent of FIG. 1A with a sinusoidalvoltage source coupled to the input; the input further coupled to theoutput.

[0018]FIG. 1C shows the circuit equivalent of FIG. 1A with a sinusoidalvoltage source coupled to the input; the output being terminated.

[0019]FIG. 2A shows a table of values of output RLCG versus frequency ascomputed from simulation results.

[0020]FIG. 2B shows a table of values of input RLCG versus frequencyprovided as input to the simulation model.

[0021]FIG. 3A shows a plot of resistance as specified, and resistancecomputed from simulation, plotted versus frequency.

[0022]FIG. 3B shows a plot of inductance as specified, and inductancecomputed from simulation, plotted versus frequency.

[0023]FIG. 3C shows a plot of dielectric conductance as specified, anddielectric conductance computed from simulation, plotted versusfrequency.

[0024]FIG. 3D shows a plot of capacitance as specified, and capacitancecomputed from simulation, plotted versus frequency.

[0025]FIG. 4 shows a block diagram of the process of calculating R(f),L(f), G(f), and C(f).

[0026]FIG. 5 shows a flow chart of an embodiment of the method ofquantitatively validating an Rline model.

[0027]FIG. 6 shows several cycles of a current and voltage versus time.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0028] Having reference now to the figures, the invention will now bedescribed in detail.

[0029] Transmission lines are used to carry electrical signals, inparticular, high-speed electrical signals. Transmission lines can becharacterized by a circuit arrangement shown in FIG. 1A. Transmissionline element 20 comprises R, L, C, and G. R represents series resistanceper unit length. L represents inductance per unit length. C representscapacitance per unit length. G represents dielectric conductance perunit length. R, L, C, G each may be frequency dependent. Resistance, forexample, rises significantly at frequencies above a gigahertz (GHz).Inductance drops with increasing frequency. Dielectric conductance riseswith increasing frequency. Capacitance is typically not a strongfunction of frequency, but, in general, may also be considered to befrequency dependent. Typically, the elements that shunt portions of anelectrical signal to ground, G and C, are divided in two with acapacitor equal to half the total capacitance per unit length placed atan input port and half placed at an output port. Similarly thedielectric conductance per unit length is typically modeled with adielectric conductance equal to half the total dielectric conductanceplaced at the input port and another dielectric conductance equal tohalf the total dielectric conductance placed at the output port. Thesignal must travel through elements, R and L between the input port andthe output port. R and L together are shown grouped as Zthru.

[0030] Modem circuit simulators typically make use of a “black box”model for transmission lines. Such models are called Rline models inthis description. As discussed earlier, these “black box” models havevarious existing names and future models could be given other names. Aparticular simulator may have the “black box” included as a built-infunction of the simulator. Alternatively, the “black box” model may bemade available as a separate piece of software that can be used. Allblack-box models of transmission lines are within the spirit and scopeof this invention, and are considered to be program products.

[0031] Users of the circuit simulator simply create an instance of theRline for each transmission line they wish to simulate. Instantiationsof the Rline typically reference a symbolic Rline model name, whichassociates characteristics of the transmission line (RLCG) values intabular form or equation form with the instantiation. The user alsotypically must supply the length of the transmission line for theinstantiation, as well as the circuit node names that the ports of theinstantiation are coupled to. For example, consider the following twoinstantiations of a transmission line model:

[0032] ms_bus_5=Rline cardline (msb5 a−msb5 b−gnd)(length=20)

[0033] ms_bus_6=Rline cardline (msb6 a−msb6 b−gnd)(length=22)

[0034] ms_bus_5 above is a user-supplied name of an instantiation of anRline model, perhaps for a main store bus bit 5. ms_bus_6 might be aninstantiation of an Rline model for bit 6 of the main store bus.

[0035] Rline tells the simulator that this model is an instantiation ofthe Rline model.

[0036] cardline associates this instantiation of the Rline model with aset of characteristics of the particular transmission line that is beingused in this instantiation. Perhaps this instantiation is for a cardsignal wire (Printed Wiring Board).

[0037] msb5 a and msb5 b are the node connections that the input andoutput signal ports of the instantiation for the main store bus bit 5are coupled to in the simulation model. msb6 a and msb6 b are the nodeconnections that the input and output signal ports of the instantiationfor the main store bus bit 6 are coupled to in the simulation model. gndis the ground voltage used in the simulation.

[0038] length is simply the length of this instantiation. For example,if length=20 and the per-unit length values are in centimeters, a 20centimeter transmission line would be modeled. Similarly, length=22would be the modeled length of the main store bus bit 6 transmissionline.

[0039] The example above is for explanation only. Different simulatorscan and do have different syntax and naming conventions. Some Rlinemodels have “ground” ports on both ends of the transmission lines,rather than the single ground port. Some Rline models have thecapability to model multiple transmission lines in a singleinstantiation so that crosstalk effects can be simulated. All variationsof the Rline model are considered to be within the spirit and scope ofthis invention.

[0040]FIG. 1B shows an instance of transmission line element 20 with theinput port shorted to the output port. A sinusoidal voltage source iscoupled to the input port. This instance, called parallel elementdetermination model 22, is used to determine the Rline model's actualeffective value of C and G, as will be described in more detail below.

[0041]FIG. 1C shows an instance of transmission line element 20. Anideal resistive terminator is coupled between the output port andground. A sinusoidal voltage source is coupled to the input port. Thisinstance, called series element determination model 24, together withparallel element determination model 22, is used to determine theRline's actual simulated value of R and L, as will be described in moredetail below.

[0042]FIGS. 2A and 2B show values of RLCG in tabular form versusfrequency. FIG. 2B shows an exemplary table of input RLCG suitable foruse as input to the Rline model. Frequency in the exemplary FIG. 2B isin GHz and ranges from 1 E-6 GHz to 10 GHz, a range suitable for mostmodern applications. The range and frequencies used can be extended tolower or higher frequencies, and more or fewer frequency points can beused. Any suitable way of providing input RLCG values versus frequencyto an Rline model is contemplated in the present invention, including,but not limited to, tables as shown, equations, and data structures.Input RLCG values are normally obtained with field solver programs thatexamine the physical sizes, shapes, and spacings of conductorsassociated with a transmission line, and the dielectric materialsseparating the conductors. The field solver program uses thisinformation, together with a programmed-in knowledge of field physics,to produce the input RLCG values versus frequency.

[0043]FIG. 2A is a table of output RLCG values computed from simulationruns. Derivation of these values will be described later. The values ofFIG. 2A are compared to the corresponding values of FIG. 2B at variousfrequencies to demonstrate how accurately the Rline model simulates thetransmission line at the various frequencies. The Rline model shouldsimulate all frequency components of a signal accurately. Rline modelsreceive a time-domain signal input from the time-domain simulator, andutilize the frequency-dependent input RLCG values and proprietaryalgorithms to produce a time-domain signal output. A predeterminedspecified agreement between the input RLCG and the output RLCG values isrequired to validate the accuracy of the Rline model. For example, auser may specify that the output RLCG values must match the input RLCGvalues within some predetermined percentage difference over a specifiedrange of frequencies. Output RLCG values that exceed the predeterminedpercentage difference require modification of the internal algorithms ofthe Rline model.

[0044] FIGS. 3A-3D show plots of the input RLCG values and the outputRLCG values versus frequency, using the exemplary data from the tablesof FIGS. 2A and 2B. Presentation in graphical form allows a means toeasily and visually detect anomalies between input RLCG values andoutput RLCG values. In the example, simulation cases at frequenciesbelow about 4 E-3 GHz were not run, as high frequency effects normallyonly occur at higher frequencies. Simulation cases at the lowerfrequencies could have been run. Simulation cases were run in theexample at substantially the same frequency points as were used in theinput RLCG data. However, this is not required, especially whenpresented in graphical form. Typically, input RLCG data makes a smoothcurve on a graph and a limited number of frequency points are required.The Rline model, however, must accurately produce time-domain modelingfor an extremely wide spectrum of frequencies. Errors in the Rline modelalgorithm may produce RLCG anomalies in only narrow bands offrequencies. Therefore, advantageously, the simulation is iterated overa large number of frequencies in an attempt to expose any Rline modeldefects that only appear in narrow frequency ranges. Alternativeembodiments of comparing input RLCG values to output RLCG include, butare not limited to, printing out large percentage difference, absolutedifferences, or use of correlation techniques done either on a dataprocessor or by manual analysis.

[0045]FIG. 3A shows a plot of input R and output R versus frequency,with data points taken at substantially the same frequencies forsimplicity. In this exemplary case, output R is shown to follow the samegeneral curve shape as input R, but is slightly higher. In the example,at approximately 4 E-1 GHz, output R is seen to be approximately oneohm/unit length, versus input R of approximately 0.6 ohm/unit length.This represents an error of about 67%. If this error exceeds thepredetermined error tolerance, the Rline model developer must correctthe algorithms used in the Rline model. It is possible that the timedomain circuit simulator might require changes, if modifications to theRline model cannot be made to bring the error within the predeterminederror tolerance. Corrections to the model, to the model/circuitsimulator interface, or the circuit simulator itself are intended, whencorrections to the Rline model discussed herein.

[0046]FIG. 3B shows a plot of input L and output L versus frequency,with data points taken at substantially the same frequencies forsimplicity. The output L is seen to exceed the input L by about 13% at 1E-2 GHz, but has much closer agreement for other frequencies. Again, ifthis anomaly exceeds predetermined error tolerance, the Rline modeldeveloper must correct the algorithms used in the Rline model.

[0047] Similarly, FIGS. 3C and 3D show plots of input G and C, andoutput C and G, versus frequency, with data points taken atsubstantially the same frequencies for simplicity. As with R and L,anomalies exceeding predetermined error tolerances must be addressed bythe Rline developer.

[0048]FIG. 4 shows, in block diagram form, the process of creating theoutput RLCG values.

[0049] A field solver, as described above, creates input RLCG tables 41.RLCG tables 41 for simple transmission lines can alternatively beproduced manually using field theory equations, or by taking data fromsimilar transmission lines' tables or graphs. The tabular format isexemplary only, and the data could be instead in the form of equations,data structures, or other techniques.

[0050] Time-domain circuit simulator 42 is given a circuit model,including an instance of parallel element determination model 22 and aninstance of series element determination model 24. In an alternativeembodiment, separate simulations are performed, one simulation on model22 by itself, and a second simulation on model 24 by itself, with datafrom both simulations to be later used to compute output RLCG.Advantageously, both model 22 and model 24 are simulated at the sametime to reduce the number of simulations required.

[0051] Run controls 43 are user-supplied controls that specify certainitems in the simulation, such as frequency, temperature, numericalconvolution parameters, outputs desired, voltages, and frequency, forexamples.

[0052] Outputs of the time-domain circuit simulator 42 simulation arestored as shown in block 44. In particular, the current I (currentthrough the sinusoidal voltage source) output from model 22 is used tocompute C and G. The Vt versus time from model 24, together with the Iversus time from model 22 is used to compute Zthru, and from that, R andL. The computations are described below, and are performed in block 45,parametric extraction of output RLCG from magnitude and phase.

[0053] Model 22 has the input port of the Rline model and the outputport of the Rline model shorted together. Since there is no voltagedifference between the ends of Zthru, no current flows through Zthru.The voltage of the sinusoidal waveform is simply impressed across thetwo dielectric conductance elements, connected in parallel and the twocapacitance elements conducted in parallel. Each dielectric conductanceelement is ½*G; each capacitive element is ½*C. Therefore the parallelcombination of the two dielectric conductance elements is G; theparallel combination of the two capacitance elements is C. The magnitudeof the sinusoidal voltage waveform is advantageously Ivolt to simplifythe math, but any suitable voltage would work. The following equationsassume a 1-volt sinusoidal input. “Re” denotes the “real” component of avector; “Im” denotes the “imaginary” component of a vector. From Ohm'sLaw: (The “(f)” denotes “for the frequency used”; f is the frequencyused)

G(f)=Re[I]  (1)

C(f)=Im[I]/(2*pi*f)  (2)

[0054] Model 24 is shown with an ideal termination resistance, Rterm,coupled between the output port of the Rline model and ground. The idealtermination resistance is highly desirable, but model 24 would still beusable without Rterm. Rterm ensures a current of a magnitude that istypically expected to flow through Zthru. For example, many transmissionlines used in data processing systems have an impedance of approximately50 ohms. Use of an Rterm of 50 ohms would be advantageous whencharacterizing such a transmission line. A 1-volt sinusoidal input isapplied to the input port of the Rline model. From Ohm's Law again,(with ω=2*pi*f)

Zthru(f)=(Vin−Vt)/(Vt/Rterm+Vt*(G/2+jω*C/2))  (3)

R(f)=Re[Zthru]  (4)

L(f)=Im[Zthru]/(2*pi*f)  (5)

[0055] The block 45 calculation of the parametric values from thesimulation data can be done directly within the circuit simulator if ithas the features to support the complex-domain mathematics if thesimulation is an “ac” run (ie, “.AC” in a Star-Hspice run). For example,in Synopsys Corporation's Star-Hspice™, in an AC simulation, imaginarycurrent through a component R1, and real voltage between nodes 7 andground can be printed using the “. PRINT” statement: (example taken fromSynopsys Corporation's Star-Hspice Manual, Release 1999.4, page 7-5)

[0056] . PRINT AC II(R1) VR(7)

[0057] Phase angles and magnitudes of voltages and currents are alsoavailable for printout in an “ac” run in available circuit simulators,such as Star-Hspice™.

[0058] However, in general, circuit simulators handle circuit elementsdifferently in an “ac” run versus a time-domain, or transient run (i.e.,“.tran” in a Star-Hspice run). It is the primary intent of thisinvention to quantitatively evaluate accuracy of the Rline model, assimulated by the time-domain simulator, in the time-domain.

[0059] Several procedures can be followed to get the real and imaginaryvalues used in equations 1-5 above, but in a time-domain, transientsimulation, where available circuit simulators do not support automaticcomputation of real and imaginary components of a vector. FIG. 6, forexample, shows a plot of voltage Vin (a 1-volt sinusoidal voltagewaveform) and I (current through the sinusoidal voltage source) as usedin model 22. The magnitude of the current I is seen graphically in theexample of FIG. 6 to be 0.7 amps. A phase angle, Θ, between current Iand Vin, in degrees, can be computed by:

Θ=ΔT/T*360  (6)

[0060] where T is the period of the sinusoidal Vin (i.e., 1/frequency),and ΔT is the difference in time between the zero crossings. ΔT could bemeasured at other points, such as at the peak magnitudes of I and Vin,but measurement at zero crossings is usually more convenient. Withmagnitude and phase angle known in the exemplary model 22 simulation, atfrequency f,

G(f)=Re[I]=magnitude(I)*cos(Θ)  (7)

C(f)=Im[I]/(2*pi*f)=magnitude(I)*sin(Θ)/(2*pi*f)  (8)

[0061] ΔT and the magnitude of current I can be manually read fromgraphical plots, or can be computed by equations programmed by the userinto the simulation to determine these values. For example, “peakdetection” equations can be used to find the magnitude of the current.Alternatively, a root mean square (RMS) value over one or more cycles ofsimulation can be computed for the current waveform; the magnitude thencomputed by dividing by 0.707 (i.e., sqrt(2)/2), as is well-known forsinusoidal waveforms.

[0062] Advantageously, a number of cycles of the Vin sinusoidal voltageare simulated at a given frequency. Averaging the magnitudes and thephase angles for more than one cycle increases the accuracy of thecomputed C and G values. Use of the very first cycle may introduceerrors involved in startup transients. Any means of determining ΔT andthe magnitude of current I are considered within the spirit ad scope ofthe present invention.

[0063] Similarly, the magnitude of (Vin-Vt) in a simulation of model 24and the phase angle between Vt and Vin can be graphically determined orcan be computed by equations programmed by the user into the simulation.

[0064] G and C were determined above for the frequency simulated; Rtermis a user-defined fixed value. Alternatively, G and C as provided in theinput RLCG data could be used in the following calculation of Zthru.Therefore, all information needed in equation (3) is available, andZthru can be computed as a vector impedance having a magnitude and aphase angle Θ. R and L at the simulated frequency f are then computedper equations (9) and (10):

R(f)=Re[Zthru]=magnitude(Zthru)*cos(Θ)  (9)

L(f)=Im[Zthru]/(2*pi*f)=magnitude(Zthru)*sin(Θ)/(2*pi*f)  (10)

[0065] The output RCLG values extracted from the simulation at the oneor more frequencies selected are placed into output RLCG tables in block46. As before, tabular format is only one way to place the values foreasy comparison with the input RLCG values. Equations, data structuresor any means suitable for storing data are within the spirit and scopeof the present invention.

[0066]FIG. 5 is a flow chart of an embodiment of the present invention.

[0067] Step 51 is simply the beginning of the process, and controlpasses to step 52.

[0068] In step 52, an Rline model is created, suitable for use by acircuit simulator. This Rline model must be capable of usingfrequency-domain input RLCG data to accurately model a transmission lineover a wide range of frequency. Algorithms used in Rline models areusually proprietary, and are not generally known to the user of thecircuit simulator. In International Business Machines's PowerSPICE, forexample, the input RLCG values (frequency dependent) are translated intocomplex propagation and admittance functions, numerically fitted, andconvolved, to yield the time-domain response voltage and current outputsfrom time-domain voltage and current inputs to the Rline model. Thenecessary numerical fitting and convolution is a known problematic areathat can introduce errors. Quantification of these errors is provided bythe method taught in the present invention.

[0069] In step 53, the user, or, more likely, a technology supportperson, prepares the frequency-dependent RLCG parameters, or values in aform suitable to be used as input to the Rline model. Most commonly, atabular format is used, but equations, data structures, or any othermeans of inputting these values to the Rline model is within the spiritand scope of the present invention. Preparation of these valuestypically involves use of a field solver and/or related programs,graphs, or tables, as described earlier.

[0070] In step 54, the user prepares a circuit simulation model suitablefor analysis by the circuit simulator of choice. A first portion of thecircuit simulation model is an instantiation of model 22, as describedearlier. This portion creates an instantiation of the Rline, with theinput and output ports of the Rline shorted together. A sinusoidalvoltage input (advantageously of 1-volt magnitude) is coupled fromground to the input port. A second portion of the circuit simulationmodel is an instantiation of model 24. In model 24, an ideal terminationis coupled between the output port of the Rline and ground. A sinusoidalvoltage input (advantageously of 1-volt magnitude) is coupled fromground to the input port. As described earlier, separate simulations canbe run on model 22 and model 24, but the number of simulations can bereduced if model 22 and model 24 are simulated at the same time.

[0071] In step 55, the circuit simulation model is simulated by thetime-domain circuit simulator at a predetermined frequency of thesinusoidal voltages in the instantiations of model 22 and model 24,using a time-domain simulation. Preferably, more than one cycle of thesinusoidal input voltages are simulated, although a single cycle is alsocontemplated and is considered within the scope of the invention.Advantageously, both voltages are at the same frequency to greatlysimplify computation of output RLCG values. Use of different frequenciesof the sinusoidal voltage inputs is possible, but complicatescomputation of output RLCG values.

[0072] In step 56, the time-domain simulation results (files, printouts,or other means of producing output by the simulator) are used to computeRLCG at the chosen frequency, as described in equations 1-5.

[0073] In step 57, a check is made to see if the circuit simulationmodel should be re-run, using another frequency for the sinusoidalvoltage inputs. If so, control is passed to step 55; if not, controlpasses to step 58.

[0074] In step 58, input RLCG values are compared to output RLCG values.As described earlier, in an embodiment of the comparison step productionof graphs is performed for visual comparison. In another embodimentmathematical correlation of the input RLCG values with the output RLCGvalues is performed. In another embodiment, secondary transmission linecharacteristics, such as frequency-dependent attenuation values, orpropagation delay values, which may be computed from the RLCG values,may be independently computed from the input RLCG and output RLCG dataand may also be compared in step 58. For example, where a isfrequency-dependent attenuation per unit length, α at a particularfrequency, f, is computed as per equation 11:

α(f)=Re|sqrt((R(f)+jωL(f))*(G(f)+jωC(f)))| where |x| indicates theabsolute value of x.  (11)

[0075] Any other means of comparing of the input RLCG values to theoutput RLCG values, as well as comparing computed secondary transmissionline characteristics, is considered within the spirit and scope of thepresent invention.

[0076] In step 59, a check is made to see if the output RLCG values arewithin a predetermined range of agreement with the input RLCG values. Ifso, the Rline model is sufficiently accurate and can be used withconfidence in further simulations of transmission lines by users of theRline model. If not, the Rline model must be fixed so that it achievesthe accuracy required. The output RLCG values and the comparison ofthose to the input RLCG values are valuable to the Rline developer incorrecting the internal algorithms of the Rline model.

[0077] An Rline model is a program product that exists on acomputer-readable medium. A program product is a set of instructionsthat, when executed on a suitable computer, causes the computer toperform the function defined by the set of instructions.Computer-readable media include, but are not limited to, magnetic disks,magnetic tapes, floppy disks, CD-ROMs, flash memory products, and datatransmission media, including the Internet. Advantageously, an Rlinemodel program product that is sold or licensed is validated as taught inthe method taught above.

[0078] While the present invention has been described with reference tothe details of the embodiments of the invention shown in the drawings,these details are not intended to limit the scope of the invention asclaimed in the appended claims.

What is claimed is:
 1. A method to quantitatively validate atransmission line model for time-domain simulation, comprising the stepsof: simulating the transmission line model at a predetermined frequency;providing a frequency dependent input transmission line characteristicusable by the transmission line model; computing an output transmissionline characteristic at the predetermined frequency using the results ofthe simulation; and comparing the output transmission linecharacteristic with the input transmission line characteristic.
 2. Themethod of claim 1, wherein the step of providing the frequency dependentinput transmission line characteristic further comprises providingresistance per unit length as the characteristic.
 3. The method of claim1, wherein the step of providing the frequency dependent inputtransmission line characteristic further comprises providing inductanceper unit length as the characteristic.
 4. The method of claim 1, whereinthe step of providing the frequency dependent input transmission linecharacteristic further comprises providing dielectric conductance perunit length as the characteristic.
 5. The method of claim 1, wherein thestep of providing the frequency dependent input transmission linecharacteristic further comprises providing capacitance per unit lengthas the characteristic.
 6. The method of claim 1, wherein the step ofcomparing the output transmission line characteristic with the inputtransmission line characteristic further comprises the steps of:computing a difference between the output transmission linecharacteristic and the input transmission line characteristic; comparingthe difference with a predetermined allowable difference; anddocumenting an excessive difference that exceeds the allowabledifference.
 7. The method of claim 6, wherein the step of comparing theoutput transmission line characteristic with the input transmission linecharacteristic further comprises comparing a secondary outputtransmission line characteristic computed from the output transmissionline characteristic with a secondary input transmission linecharacteristic computed from the input transmission line characteristic.8. The method of claim 6, further comprising the step of: iterating thesimulation for a predetermined set of frequencies.
 9. The method ofclaim 8, further comprising the steps of: plotting the inputtransmission line characteristic versus frequency; and plotting theoutput transmission line characteristic versus frequency for frequenciesin the predetermined set of frequencies.
 10. The method of claim 1, inwhich the step of simulating the transmission line model in thetime-domain further comprises the steps of: simulating a first instanceof the transmission line model in which an input port of the firstinstance is coupled to an output port of the first instance, and inwhich a sinusoidal voltage source is coupled to the input port of thefirst instance; and simulating a second instance of the transmissionline model in which a sinusoidal voltage source is coupled to an inputport of the second instance.
 11. The method of claim 10, in which thestep of simulating the second instance further comprises coupling atermination resistance to an output port of the second instance of thetransmission line.
 12. The method of claim 10, in which the step ofusing results of the simulation to compute an output transmission linecharacteristic at the predetermined frequency further comprises the stepof computing a value of capacitance per unit length using a magnitude ofa current through the sinusoidal voltage source of the first instance ofthe transmission line model, and a phase angle between the current andthe sinusoidal voltage.
 13. The method of claim 10, in which the step ofusing results of the simulation to compute an output transmission linecharacteristic at the predetermined frequency further comprises the stepof computing a value of dielectric conductance per unit length using amagnitude of a current through the sinusoidal voltage source of thefirst instance of the transmission line model, and a phase angle betweenthe current and the sinusoidal voltage.
 14. The method of claim 10, inwhich the step of using results of the simulation to compute an outputtransmission line characteristic at the predetermined frequency furthercomprises the step of computing a value of resistance per unit lengthusing a magnitude of a difference between a voltage on the output portof the second instance of the transmission line model and the sinusoidalvoltage coupled to the input port of the second instance of thetransmission line model, and the phase angle between the voltage on theoutput port of the second instance and the sinusoidal voltage coupled tothe input port of the second instance.
 15. The method of claim 10, inwhich the step of using results of the simulation to compute an outputtransmission line characteristic at the predetermined frequency furthercomprises the step of computing a value of inductance per unit lengthusing a magnitude of a difference between a voltage on the output portof the second instance of the transmission line model and the sinusoidalvoltage coupled to the input port of the second instance of thetransmission line model, and the phase angle between the voltage on theoutput port of the second instance and the sinusoidal voltage coupled tothe input port of the second instance.
 16. A program product comprisinga transmission line model validated by the method of claim
 1. 17. Aprogram product comprising a transmission line model, the model beingvalidated by the following steps: simulating the transmission line modelin the time-domain, at a predetermined frequency, using a circuitsimulator; providing a frequency dependent input transmission linecharacteristic usable by the transmission line model; using results ofthe simulation to compute an output transmission line characteristic atthe predetermined frequency; and comparing the output transmission linecharacteristic with the input transmission line characteristic.